题目：Regularized Kaczmarz Algorithms for High-Order Tensor Recovery

汇报人：秦菁

汇报时间：2024年 6月24日（周一）13：30-15：00

地点：综合楼644会议室

报告人简介： 

研究方向包括图像处理，最优化，基于图论的数据分析，和高维线性代数及其应用。研究成果发表在SIAM Journal on Imaging Sciences, Journal of Scientific Computing, Inverse Problems and Imaging, IEEE Transactions on Geoscience and Remote Sensing， IEEE Transactions on 等 期刊，和IEEE IGARSS, ISBI, EMBC, ICMA等相关会议。

摘要：

Tensors serve as a crucial tool in the representation and analysis of complex, multi-dimensional data. As data volumes continue to expand, there is an increasing demand for developing optimization algorithms that can directly operate on tensors to deliver fast and effective computations. Many problems in real-world applications can be formulated as the task of recovering high-order tensors characterized by sparse and/or low-rank structures. In this work, we propose novel Kaczmarz algorithms with two regularization techniques for reconstructing high-order tensors by exploiting sparsity and/or low-rankness of tensor data. In addition, we develop both a block and an accelerated variant, along with a thorough convergence analysis of these algorithms. A variety of numerical experiments on both synthetic and real-world datasets demonstrate the effectiveness and significant potential of the proposed methods in image and video processing tasks, such as image sequence destriping and video deconvolution.